Dynamic and continuously evolving environments present significant challenges for robotic mapping and scene understanding, particularly on construction sites where moving agents, temporary obstacles, and persistent structural changes coexist. While dynamic and long-term SLAM methods can detect motion and environmental changes, their outputs are predominantly metric representations that provide limited structure for higher-level spatial and temporal reasoning. This paper presents a LiDAR-based real-time temporal construction scene graph (T-ConSG) that jointly represents free-space regions, static objects, dynamic objects, and environmental events with spatial-relational and event-participation edges. The proposed framework incrementally constructs the graph from LiDAR-derived geometric evidence, maintaining persistent free-space and static-object information while tracking dynamic objects. Changes in accumulated spatial evidence are further represented as explicit installation and removal events, allowing the graph to capture both transient dynamics and persistent environmental evolution. We demonstrate the proposed representation through three complementary application studies: dynamics-aware navigation in a bricklaying testbed, construction progress monitoring on the ConSLAM dataset, and online change detection in a simulated construction environment. The results demonstrate that the proposed T-ConSG provides a unified representation for organizing spatial and temporal information and supports robotic reasoning across environments containing both short-term dynamics and persistent changes.

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